Common questions

Does the atlas list all groups or all representations?

The classification views describe their declared families. Individual records and executable capabilities have separate coverage. Finite summaries may be complete for ordinary complex irrep dimensions while other representation data remain unavailable. Lie-group highest weights describe infinite families; the workbench browser has an explicit dimension cutoff.

Why are group and algebra searches separate?

Groups with the same local algebra can have different centers, fundamental groups, and representation descent conditions. A real algebra and its complexification also carry different data. Search results preserve these types.

Why does branching require a map?

The same abstract subgroup can occur through inequivalent maps. The regular and principal SU(3) examples have different kernels and different decompositions.

Does a singlet count give every physical interaction?

It counts invariants in the declared tensor space. Field species, statistics, Lorentz structure, additional charges, and derivative relations can change the physical operator problem. The A₄ example makes the distinction explicit.

Does a topology calculation prove a soliton exists?

The supported homotopy sequence supplies topological-sector information for the specified spaces and maps. Existence, finite energy, and stability require dynamical analysis.

What does “expert review pending” mean?

Sources and automatic checks have been recorded, while independent human mathematics and physics review has not been completed for the current content fingerprint. These are separately recorded forms of evidence. See the editorial method.